Quantum cascade lasers (QCLs) are made of stages each of which is composed of three regions: an electron injector, an active region and an electron extractor. In conventional QCLs, the quantum wells and barriers in all regions are of the same, fixed alloy composition, respectively. In addition, for short wavelength (λ˜4.6-4.8 μm) QCLs operated around room temperature, the electrons in the injector and upper laser level are found to have a higher temperature than that of the lattice—that is, they are hot. See D. Botez et al., Proc. SPIE Novel In-Plane Semiconductor Lasers X Conf. 7953, 79530N (2011); D. Botez et al., Proc. SPIE 8277, 82770W (2012). Consequently, conventional QCLs emitting in the 4.5-5.0 μm range experience substantial electron leakage which results in low characteristic-temperature T0 values (e.g., ˜140 K) for the threshold-current density, Jth, and low characteristic-temperature T1 (e.g., ˜140K) values for the slope efficiency, ηsl at heatsink temperatures above room temperature. Id. As a result, the maximum wallplug efficiency ηwp,max in continuous wave (CW) operation at room temperature (for light emitted at 300 K from the front facet of devices with high-reflectivity-coated back facets) has typical values that fall far short (e.g., 13%) of the theoretically predicted upper limit of ˜32% at λ=4.6 μm. See D. Botez et al., Proc. SPIE Novel In-Plane Semiconductor Lasers X Conf. 7953, 79530N (2011). Other designs for QCLs have been proposed to address the issue of electron leakage. However, in order to maximize efficiencies, designs which further suppress electron leakage and reduce threshold-current density are needed.